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We extend this result to digraphs by showing that if $D$ is a digraph with $n$ vertices, then $ \\alpha(D)\\geq \\sum_{i=1}^n \\left( \\frac{1}{1+d_i^+} + \\frac{1}{1+d_i^-}\n  - \\frac{1}{1+d_i}\\right)$, where $\\alpha(D)$ is the maximum size of an acyclic vertex set of $D$. Golowich proved that for any digraph $D$, $\\chi(D)\\leq \\lceil \\frac{4k}{5} \\rceil+2$, where $k=max(\\Delta^+(D),\\Delta^-(D))$. 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It is well-known that $\\alpha(G)\\geq \\sum_{i=1}^n \\frac{1}{1+d_i}$, where $\\alpha(G)$ is the independence number of $G$ and $d_1,\\ldots,d_n$ is the degree sequence of $G$. We extend this result to digraphs by showing that if $D$ is a digraph with $n$ vertices, then $ \\alpha(D)\\geq \\sum_{i=1}^n \\left( \\frac{1}{1+d_i^+} + \\frac{1}{1+d_i^-}\n  - \\frac{1}{1+d_i}\\right)$, where $\\alpha(D)$ is the maximum size of an acyclic vertex set of $D$. Golowich proved that for any digraph $D$, $\\chi(D)\\leq \\lceil \\frac{4k}{5} \\rceil+2$, where $k=max(\\Delta^+(D),\\Delta^-(D))$. 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